On mask selection for time-varying filtering using the Wigner distribution

The application of a multiplicative modification function, or mask, to the Wigner distribution (WD) of a signal has been proposed as an implementation of time-varying filtering in the time-frequency plane. Because the least squares synthesis technique involves an eigenvalue/eigenvector decomposition, the effects of mask size, shape, and placement on the reconstructed system output are not well understood. However, for the case of a Gaussian input signal and a Gaussian shaped mask, the result of the least squares synthesis procedure on the modified WD can be expressed analytically. This expression for the system output is a function of the input signal and mask Gaussian parameters and can be used to analyze the effects of the mask on the output. For masks that are smaller than the WD of the input, the reconstructed signal has a WD related to the mask and not the system input